RFC 2875

Network Working Group H. Prafullchandra
Request for Comments: 2875 Critical Path Inc
Category: Standards Track J. Schaad
July 2000
Diffie-Hellman Proof-of-Possession Algorithms
Status of this Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2000). All Rights Reserved.
Abstract
This document describes two methods for producing an integrity check
value from a Diffie-Hellman key pair. This behavior is needed for
such operations as creating the signature of a PKCS #10 certification
request. These algorithms are designed to provide a proof-of-
possession rather than general purpose signing.
1. Introduction
PKCS #10 [RFC2314] defines a syntax for certification requests. It
assumes that the public key being requested for certification
corresponds to an algorithm that is capable of signing/encrypting.
Diffie-Hellman (DH) is a key agreement algorithm and as such cannot
be directly used for signing or encryption.
This document describes two new proof-of-possession algorithms using
the Diffie-Hellman key agreement process to provide a shared secret
as the basis of an integrity check value. In the first algorithm,
the value is constructed for a specific recipient/verifier by using a
public key of that verifier. In the second algorithm, the value is
constructed for arbitrary verifiers.
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
2. Terminology
The following definitions will be used in this document
DH certificate = a certificate whose SubjectPublicKey is a DH public
value and is signed with any signature algorithm (e.g. RSA or DSA).
3. Static DH Proof-of-Possession Process
The steps for creating a DH POP are:
1. An entity (E) chooses the group parameters for a DH key
agreement.
This is done simply by selecting the group parameters from a
certificate for the recipient of the POP process.
A certificate with the correct group parameters has to be
available. Let these common DH parameters be g and p; and let
this DH key-pair be known as the Recipient key pair (Rpub and
Rpriv).
Rpub = g^x mod p (where x=Rpriv, the private DH value and
^ denotes exponentiation)
2. The entity generates a DH public/private key-pair using the
parameters from step 1.
For an entity E:
Epriv = DH private value = y
Epub = DH public value = g^y mod p
3. The POP computation process will then consist of:
a) The value to be signed is obtained. (For a RFC2314 object, the
value is the DER encoded certificationRequestInfo field
represented as an octet string.) This will be the `text'
referred to in [RFC2104], the data to which HMAC-SHA1 is
applied.
b) A shared DH secret is computed, as follows,
shared secret = ZZ = g^xy mod p
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
[This is done by the entity E as Rpub^y and by the Recipient
as Epub^x, where Rpub is retrieved from the Recipient's DH
certificate (or is the one that was locally generated by the
Entity) and Epub is retrieved from the actual certification
request.]
c) A temporary key K is derived from the shared secret ZZ as
follows:
K = SHA1(LeadingInfo | ZZ | TrailingInfo),
where "|" means concatenation.
LeadingInfo ::= Subject Distinguished Name from certificate
TrailingInfo ::= Issuer Distinguished Name from certificate
d) Compute HMAC-SHA1 over the data `text' as per [RFC2104] as:
SHA1(K XOR opad, SHA1(K XOR ipad, text))
where,
opad (outer pad) = the byte 0x36 repeated 64 times and
ipad (inner pad) = the byte 0x5C repeated 64 times.
Namely,
(1) Append zeros to the end of K to create a 64 byte string
(e.g., if K is of length 16 bytes it will be appended
with 48 zero bytes 0x00).
(2) XOR (bitwise exclusive-OR) the 64 byte string computed
in step (1) with ipad.
(3) Append the data stream `text' to the 64 byte string
resulting from step (2).
(4) Apply SHA1 to the stream generated in step (3).
(5) XOR (bitwise exclusive-OR) the 64 byte string computed
in step (1) with opad.
(6) Append the SHA1 result from step (4) to the 64 byte
string resulting from step (5).
(7) Apply SHA1 to the stream generated in step (6) and
output the result.
Sample code is also provided in [RFC2104].
e) The output of (d) is encoded as a BIT STRING (the Signature
value).
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
The POP verification process requires the Recipient to carry out
steps (a) through (d) and then simply compare the result of step (d)
with what it received as the signature component. If they match then
the following can be concluded:
a) The Entity possesses the private key corresponding to the
public key in the certification request because it needed the
private key to calculate the shared secret; and
b) Only the Recipient that the entity sent the request to could
actually verify the request because they would require their
own private key to compute the same shared secret. In the case
where the recipient is a Certification Authority, this
protects the Entity from rogue CAs.
ASN Encoding
The ASN.1 structures associated with the static Diffie-Hellman POP
algorithm are:
id-dhPop-static-HMAC-SHA1 OBJECT IDENTIFIER ::= { id-pkix
id-alg(6) 3}
DhPopStatic ::= SEQUENCE {
issuerAndSerial IssuerAndSerialNumber OPTIONAL,
hashValue MessageDigest
}
issuerAndSerial is the issuer name and serial number of the
certificate from which the public key was obtained. The
issuerAndSerial field is omitted if the public key did not come
from a certificate.
hashValue contains the result of the SHA-1 HMAC operation in step
3d.
DhPopStatic is encoded as a BIT STRING and is the signature value
(i.e. encodes the above sequence instead of the raw output from 3d).
4. Discrete Logarithm Signature
The use of a single set of parameters for an entire public key
infrastructure allows all keys in the group to be attacked together.
For this reason we need to create a proof of possession for Diffie-
Hellman keys that does not require the use of a common set of
parameters.
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
This POP is based on the Digital Signature Algorithm, but we have
removed the restrictions imposed by the [FIPS-186] standard. The use
of this method does impose some additional restrictions on the set of
keys that may be used, however if the key generation algorithm
documented in [DH-X9.42] is used the required restrictions are met.
The additional restrictions are the requirement for the existence of
a q parameter. Adding the q parameter is generally accepted as a good
practice as it allows for checking of small group attacks.
The following definitions are used in the rest of this section:
p is a large prime
g = h(p-1)/q mod p ,
where h is any integer 1 < h < p-1 such that h(p-1) mod q > 1
(g has order q mod p)
q is a large prime
j is a large integer such that p = qj + 1
x is a randomly or pseudo-randomly generated integer with
1 < x < q
y = g^x mod p
Note: These definitions match the ones in [DH-X9.42].
4.1 Expanding the Digest Value
Besides the addition of a q parameter, [FIPS-186] also imposes size
restrictions on the parameters. The length of q must be 160-bits
(matching output of the SHA-1 digest algorithm) and length of p must
be 1024-bits. The size restriction on p is eliminated in this
document, but the size restriction on q is replaced with the
requirement that q must be at least 160-bits. (The size restriction
on q is identical with that in [DH-X9.42].)
Given that there is not a random length-hashing algorithm, a hash
value of the message will need to be derived such that the hash is in
the range from 0 to q-1. If the length of q is greater than 160-bits
then a method must be provided to expand the hash length.
The method for expanding the digest value used in this section does
not add any additional security beyond the 160-bits provided by SHA-
1. The value being signed is increased mainly to enhance the
difficulty of reversing the signature process.
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
This algorithm produces m the value to be signed.
Let L = the size of q (i.e. 2^L <= q < 2^(L+1)). Let M be the
original message to be signed.
1. Compute d = SHA-1(M), the SHA-1 digest of the original message.
2. If L == 160 then m = d.
3. If L > 160 then follow steps (a) through (d) below.
a) Set n = L / 160, where / represents integer division,
consequently, if L = 200, n = 1.
b) Set m = d, the initial computed digest value.
c) For i = 0 to n - 1
m = m | SHA(m), where "|" means concatenation.
d) m = LEFTMOST(m, L-1), where LEFTMOST returns the L-1 left most
bits of m.
Thus the final result of the process meets the criteria that 0 <= m <
q.
4.2 Signature Computation Algorithm
The signature algorithm produces the pair of values (r, s), which is
the signature. The signature is computed as follows:
Given m, the value to be signed, as well as the parameters defined
earlier in section 5.
1. Generate a random or pseudorandom integer k, such that 0 < k^-1 <
q.
2. Compute r = (g^k mod p) mod q.
3. If r is zero, repeat from step 1.
4. Compute s = (k^-1 (m + xr)) mod q.
5. If s is zero, repeat from step 1.
4.3 Signature Verification Algorithm
The signature verification process is far more complicated than is
normal for the Digital Signature Algorithm, as some assumptions about
the validity of parameters cannot be taken for granted.
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
Given a message m to be validated, the signature value pair (r, s)
and the parameters for the key.
1. Perform a strong verification that p is a prime number.
2. Perform a strong verification that q is a prime number.
3. Verify that q is a factor of p-1, if any of the above checks fail
then the signature cannot be verified and must be considered a
failure.
4. Verify that r and s are in the range [1, q-1].
5. Compute w = (s^-1) mod q.
6. Compute u1 = m*w mod q.
7. Compute u2 = r*w mod q.
8. Compute v = ((g^u1 * y^u2) mod p) mod q.
9. Compare v and r, if they are the same then the signature verified
correctly.
4.4 ASN Encoding
The signature is encoded using
id-alg-dhPOP OBJECT IDENTIFIER ::= {id-pkix id-alg(6) 4}
The parameters for id-alg-dhPOP are encoded as DomainParameters
(imported from [PROFILE]). The parameters may be omitted in the
signature, as they must exist in the associated key request.
The signature value pair r and s are encoded using Dss-Sig-Value
(imported from [PROFILE]).
5. Security Considerations
In the static DH POP algorithm, an appropriate value can be produced
by either party. Thus this algorithm only provides integrity and not
origination service. The Discrete Logarithm algorithm provides both
integrity checking and origination checking.
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
All the security in this system is provided by the secrecy of the
private keying material. If either sender or recipient private keys
are disclosed, all messages sent or received using that key are
compromised. Similarly, loss of the private key results in an
inability to read messages sent using that key.
Selection of parameters can be of paramount importance. In the
selection of parameters one must take into account the
community/group of entities that one wishes to be able to communicate
with. In choosing a set of parameters one must also be sure to avoid
small groups. [FIPS-186] Appendixes 2 and 3 contain information on
the selection of parameters. The practices outlined in this document
will lead to better selection of parameters.
6. References
[FIPS-186] Federal Information Processing Standards Publication
(FIPS PUB) 186, "Digital Signature Standard", 1994 May
19.
[RFC2314] Kaliski, B., "PKCS #10: Certification Request Syntax
v1.5", RFC 2314, October 1997.
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104, February
1997.
[PROFILE] Housley, R., Ford, W., Polk, W., and D. Solo, "Internet
X.509 Public Key Infrastructure: Certificate and CRL
Profile", RFC 2459, January 1999.
[DH-X9.42] Rescorla, E., "Diffie-Hellman Key Agreement Method", RFC
2631, June 1999.
7. Authors' Addresses
Hemma Prafullchandra
Critical Path Inc.
5150 El Camino Real, #A-32
Los Altos, CA 94022
Phone: (640) 694-6812
EMail: hemma@cp.net
Jim Schaad
EMail: jimsch@exmsft.com
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RFC 2875 Diffie-Hellman Proof-of-Possession Algorithms July 2000
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